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3 years ago

Converse of the pythagorean therom

Mathematics

2 answers:

Sphinxa [80]3 years ago

3 0

The pythagorean theorem states that if a triangle is a right triangle, then the sum of the squares of the legs of the triangle is equal to the square of the hypotenuse or a² + b² = c².

The converse of the pythagorean theorem on the other hand states that if the sum of the squares of 2 sides of a triangle is equal to the square of the third side or a² + b² = c², then the triangle is a right triangle.

The converse switches the order of the if and then statements.

On the whiteboard, I have also written it.

Image provided.

Murljashka [212]3 years ago

3 0

“if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle”

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The weekly salary of a store manager includes a $30 bonus plus the number of hours the manager works multiplied by the managers

gizmo_the_mogwai [7]

Yes. The situation is defined by a linear function.

Solution:

Given, The weekly salary of a store manager includes a $30 bonus plus the number of hours the manager works multiplied by the managers earnings per hour.

Is this situation defined by a linear function?

Yes, the above given situation is defined by a linear function.

Now, let us see the linear equation for above situation

Let the number of hours worked by manager be "x", and cost per hour be "c" and total salary be "y"

Then, total salary is given as,

Total salary = $ 30 bonus + number of hours worked $\times$ cost per hour

$\rightarrow \mathrm{y}=30+\mathrm{x} \times \mathrm{c}\\\\ \rightarrow \mathrm{y}=\mathrm{c} \mathrm{x}+30$

Above equation is a linear equation as "c" is constant ( cost per hour )

Hence, the given situation can be defined by linear function.

5 0

3 years ago

Please help! Please explain how to do this, I am so lost.

alexdok [17]

Ok, so we know that RST is equal to 6x+12
And RST is also equal to 78 + 3x-12
so we set them equal to each other

6x + 12 = 3x - 12 + 78
And simplify
3x = 54
x = 18

Finally, we solve for the angle with 18 for x

6(18) + 12
108 + 12
120

Hope this helps

8 0

3 years ago

3 + 12c - 4c What is the answer I need help?

HACTEHA [7]

Your answer is 3 + 8c!!

7 0

3 years ago

A pharmacist has 80 milileters of a 25 percent saline solution. Which expression can be used to find the percentage of the conce

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

Final concentration % = [grams of salt / mililiters of solution] * 100

grams of salt = grams of salt from solution 1 + grams of salt from solution 2

grams of salt from solution 1 = mililiters * %/100 = 80 mililiters * 0.25 g/mililiters = 20 g

grams of salt from solution 2 = mililiters *%/100 = x*0.10 g/mililiters = 0.1x

mililiters of final solution = mililiters from solution 1 + mililiters from solution 2

mililiters of final solution = 80 mililiters + x mililiters

=> Final concentration, % = [0,10x + 20 g] / [x + 80 mililiters] * 100

6 0

3 years ago

The mass of a bacteria culture doubles every four days. If the initial sample is 5mg: a) how much will you have after one week (

maks197457 [2]

Answer:

a) 16.82 mg

b) 24 days

Step-by-step explanation:

Formula for exponential growth is given as:

$A=A_0b^{\frac{t}{c}}$

Where A is the final population

$A_0$ is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, We are given the following:

$A_0$ = 5 mg

b = 2 (Given because it doubles)

c = 4 days

a) A = ?

Using the formula:

$A=5 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}$

b) Given

A = 320 mg

t = ?

Using the above formula again:

$320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}$

So, the answers are:

a) 16.82 mg

b) 24 days

6 0

3 years ago